COIN-OR::LEMON - Graph Library

source: lemon-1.2/doc/groups.dox @ 609:e6927fe719e6

Last change on this file since 609:e6927fe719e6 was 609:e6927fe719e6, checked in by Peter Kovacs <kpeter@…>, 11 years ago

Support >= and <= constraints in NetworkSimplex? (#219, #234)

By default the same inequality constraints are supported as by
Circulation (the GEQ form), but the LEQ form can also be selected
using the problemType() function.

The documentation of the min. cost flow module is reworked and
extended with important notes and explanations about the different
variants of the problem and about the dual solution and optimality

File size: 26.2 KB
[209]1/* -*- mode: C++; indent-tabs-mode: nil; -*-
[40]2 *
[209]3 * This file is a part of LEMON, a generic C++ optimization library.
[40]4 *
[440]5 * Copyright (C) 2003-2009
[40]6 * Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport
7 * (Egervary Research Group on Combinatorial Optimization, EGRES).
8 *
9 * Permission to use, modify and distribute this software is granted
10 * provided that this copyright notice appears in all copies. For
11 * precise terms see the accompanying LICENSE file.
12 *
13 * This software is provided "AS IS" with no warranty of any kind,
14 * express or implied, and with no claim as to its suitability for any
15 * purpose.
16 *
17 */
[406]19namespace lemon {
22@defgroup datas Data Structures
[50]23This group describes the several data structures implemented in LEMON.
27@defgroup graphs Graph Structures
28@ingroup datas
29\brief Graph structures implemented in LEMON.
[209]31The implementation of combinatorial algorithms heavily relies on
32efficient graph implementations. LEMON offers data structures which are
33planned to be easily used in an experimental phase of implementation studies,
34and thereafter the program code can be made efficient by small modifications.
36The most efficient implementation of diverse applications require the
37usage of different physical graph implementations. These differences
38appear in the size of graph we require to handle, memory or time usage
39limitations or in the set of operations through which the graph can be
40accessed.  LEMON provides several physical graph structures to meet
41the diverging requirements of the possible users.  In order to save on
42running time or on memory usage, some structures may fail to provide
[83]43some graph features like arc/edge or node deletion.
[209]45Alteration of standard containers need a very limited number of
46operations, these together satisfy the everyday requirements.
47In the case of graph structures, different operations are needed which do
48not alter the physical graph, but gives another view. If some nodes or
[83]49arcs have to be hidden or the reverse oriented graph have to be used, then
[209]50this is the case. It also may happen that in a flow implementation
51the residual graph can be accessed by another algorithm, or a node-set
52is to be shrunk for another algorithm.
53LEMON also provides a variety of graphs for these requirements called
54\ref graph_adaptors "graph adaptors". Adaptors cannot be used alone but only
55in conjunction with other graph representations.
57You are free to use the graph structure that fit your requirements
58the best, most graph algorithms and auxiliary data structures can be used
[314]59with any graph structure.
61<b>See also:</b> \ref graph_concepts "Graph Structure Concepts".
[451]65@defgroup graph_adaptors Adaptor Classes for Graphs
[416]66@ingroup graphs
[451]67\brief Adaptor classes for digraphs and graphs
69This group contains several useful adaptor classes for digraphs and graphs.
71The main parts of LEMON are the different graph structures, generic
[451]72graph algorithms, graph concepts, which couple them, and graph
[416]73adaptors. While the previous notions are more or less clear, the
74latter one needs further explanation. Graph adaptors are graph classes
75which serve for considering graph structures in different ways.
77A short example makes this much clearer.  Suppose that we have an
[451]78instance \c g of a directed graph type, say ListDigraph and an algorithm
80template <typename Digraph>
81int algorithm(const Digraph&);
83is needed to run on the reverse oriented graph.  It may be expensive
84(in time or in memory usage) to copy \c g with the reversed
85arcs.  In this case, an adaptor class is used, which (according
[451]86to LEMON \ref concepts::Digraph "digraph concepts") works as a digraph.
87The adaptor uses the original digraph structure and digraph operations when
88methods of the reversed oriented graph are called.  This means that the adaptor
89have minor memory usage, and do not perform sophisticated algorithmic
[416]90actions.  The purpose of it is to give a tool for the cases when a
91graph have to be used in a specific alteration.  If this alteration is
[451]92obtained by a usual construction like filtering the node or the arc set or
[416]93considering a new orientation, then an adaptor is worthwhile to use.
94To come back to the reverse oriented graph, in this situation
96template<typename Digraph> class ReverseDigraph;
98template class can be used. The code looks as follows
100ListDigraph g;
[451]101ReverseDigraph<ListDigraph> rg(g);
[416]102int result = algorithm(rg);
[451]104During running the algorithm, the original digraph \c g is untouched.
105This techniques give rise to an elegant code, and based on stable
[416]106graph adaptors, complex algorithms can be implemented easily.
[451]108In flow, circulation and matching problems, the residual
[416]109graph is of particular importance. Combining an adaptor implementing
[451]110this with shortest path algorithms or minimum mean cycle algorithms,
[416]111a range of weighted and cardinality optimization algorithms can be
112obtained. For other examples, the interested user is referred to the
113detailed documentation of particular adaptors.
115The behavior of graph adaptors can be very different. Some of them keep
116capabilities of the original graph while in other cases this would be
[451]117meaningless. This means that the concepts that they meet depend
118on the graph adaptor, and the wrapped graph.
119For example, if an arc of a reversed digraph is deleted, this is carried
120out by deleting the corresponding arc of the original digraph, thus the
121adaptor modifies the original digraph.
122However in case of a residual digraph, this operation has no sense.
124Let us stand one more example here to simplify your work.
[451]125ReverseDigraph has constructor
127ReverseDigraph(Digraph& digraph);
[451]129This means that in a situation, when a <tt>const %ListDigraph&</tt>
[416]130reference to a graph is given, then it have to be instantiated with
[451]131<tt>Digraph=const %ListDigraph</tt>.
133int algorithm1(const ListDigraph& g) {
[451]134  ReverseDigraph<const ListDigraph> rg(g);
[416]135  return algorithm2(rg);
[50]141@defgroup semi_adaptors Semi-Adaptor Classes for Graphs
[40]142@ingroup graphs
143\brief Graph types between real graphs and graph adaptors.
[50]145This group describes some graph types between real graphs and graph adaptors.
[209]146These classes wrap graphs to give new functionality as the adaptors do it.
[50]147On the other hand they are not light-weight structures as the adaptors.
[209]151@defgroup maps Maps
[40]152@ingroup datas
[50]153\brief Map structures implemented in LEMON.
[50]155This group describes the map structures implemented in LEMON.
[314]157LEMON provides several special purpose maps and map adaptors that e.g. combine
[40]158new maps from existing ones.
160<b>See also:</b> \ref map_concepts "Map Concepts".
[209]164@defgroup graph_maps Graph Maps
[40]165@ingroup maps
[83]166\brief Special graph-related maps.
[50]168This group describes maps that are specifically designed to assign
[406]169values to the nodes and arcs/edges of graphs.
171If you are looking for the standard graph maps (\c NodeMap, \c ArcMap,
172\c EdgeMap), see the \ref graph_concepts "Graph Structure Concepts".
176\defgroup map_adaptors Map Adaptors
177\ingroup maps
178\brief Tools to create new maps from existing ones
[50]180This group describes map adaptors that are used to create "implicit"
181maps from other maps.
[406]183Most of them are \ref concepts::ReadMap "read-only maps".
[83]184They can make arithmetic and logical operations between one or two maps
185(negation, shifting, addition, multiplication, logical 'and', 'or',
186'not' etc.) or e.g. convert a map to another one of different Value type.
[50]188The typical usage of this classes is passing implicit maps to
[40]189algorithms.  If a function type algorithm is called then the function
190type map adaptors can be used comfortable. For example let's see the
[314]191usage of map adaptors with the \c graphToEps() function.
193  Color nodeColor(int deg) {
194    if (deg >= 2) {
195      return Color(0.5, 0.0, 0.5);
196    } else if (deg == 1) {
197      return Color(1.0, 0.5, 1.0);
198    } else {
199      return Color(0.0, 0.0, 0.0);
200    }
201  }
[83]203  Digraph::NodeMap<int> degree_map(graph);
[314]205  graphToEps(graph, "graph.eps")
[40]206    .coords(coords).scaleToA4().undirected()
[83]207    .nodeColors(composeMap(functorToMap(nodeColor), degree_map))
[40]208    .run();
[83]210The \c functorToMap() function makes an \c int to \c Color map from the
[314]211\c nodeColor() function. The \c composeMap() compose the \c degree_map
[83]212and the previously created map. The composed map is a proper function to
213get the color of each node.
215The usage with class type algorithms is little bit harder. In this
216case the function type map adaptors can not be used, because the
[50]217function map adaptors give back temporary objects.
[83]219  Digraph graph;
221  typedef Digraph::ArcMap<double> DoubleArcMap;
222  DoubleArcMap length(graph);
223  DoubleArcMap speed(graph);
225  typedef DivMap<DoubleArcMap, DoubleArcMap> TimeMap;
[40]226  TimeMap time(length, speed);
[83]228  Dijkstra<Digraph, TimeMap> dijkstra(graph, time);
[40]229, target);
[83]231We have a length map and a maximum speed map on the arcs of a digraph.
232The minimum time to pass the arc can be calculated as the division of
233the two maps which can be done implicitly with the \c DivMap template
[40]234class. We use the implicit minimum time map as the length map of the
235\c Dijkstra algorithm.
[209]239@defgroup matrices Matrices
[40]240@ingroup datas
[50]241\brief Two dimensional data storages implemented in LEMON.
[50]243This group describes two dimensional data storages implemented in LEMON.
247@defgroup paths Path Structures
248@ingroup datas
[318]249\brief %Path structures implemented in LEMON.
[50]251This group describes the path structures implemented in LEMON.
[50]253LEMON provides flexible data structures to work with paths.
254All of them have similar interfaces and they can be copied easily with
255assignment operators and copy constructors. This makes it easy and
[40]256efficient to have e.g. the Dijkstra algorithm to store its result in
257any kind of path structure.
259\sa lemon::concepts::Path
263@defgroup auxdat Auxiliary Data Structures
264@ingroup datas
[50]265\brief Auxiliary data structures implemented in LEMON.
[50]267This group describes some data structures implemented in LEMON in
[40]268order to make it easier to implement combinatorial algorithms.
272@defgroup algs Algorithms
273\brief This group describes the several algorithms
274implemented in LEMON.
276This group describes the several algorithms
277implemented in LEMON.
281@defgroup search Graph Search
282@ingroup algs
[50]283\brief Common graph search algorithms.
[406]285This group describes the common graph search algorithms, namely
286\e breadth-first \e search (BFS) and \e depth-first \e search (DFS).
[314]290@defgroup shortest_path Shortest Path Algorithms
[40]291@ingroup algs
[50]292\brief Algorithms for finding shortest paths.
[406]294This group describes the algorithms for finding shortest paths in digraphs.
296 - \ref Dijkstra algorithm for finding shortest paths from a source node
297   when all arc lengths are non-negative.
298 - \ref BellmanFord "Bellman-Ford" algorithm for finding shortest paths
299   from a source node when arc lenghts can be either positive or negative,
300   but the digraph should not contain directed cycles with negative total
301   length.
302 - \ref FloydWarshall "Floyd-Warshall" and \ref Johnson "Johnson" algorithms
303   for solving the \e all-pairs \e shortest \e paths \e problem when arc
304   lenghts can be either positive or negative, but the digraph should
305   not contain directed cycles with negative total length.
306 - \ref Suurballe A successive shortest path algorithm for finding
307   arc-disjoint paths between two nodes having minimum total length.
[314]311@defgroup max_flow Maximum Flow Algorithms
[209]312@ingroup algs
[50]313\brief Algorithms for finding maximum flows.
315This group describes the algorithms for finding maximum flows and
316feasible circulations.
[406]318The \e maximum \e flow \e problem is to find a flow of maximum value between
319a single source and a single target. Formally, there is a \f$G=(V,A)\f$
[609]320digraph, a \f$cap: A\rightarrow\mathbf{R}^+_0\f$ capacity function and
[406]321\f$s, t \in V\f$ source and target nodes.
[609]322A maximum flow is an \f$f: A\rightarrow\mathbf{R}^+_0\f$ solution of the
[406]323following optimization problem.
[609]325\f[ \max\sum_{sv\in A} f(sv) - \sum_{vs\in A} f(vs) \f]
326\f[ \sum_{uv\in A} f(uv) = \sum_{vu\in A} f(vu)
327    \quad \forall u\in V\setminus\{s,t\} \f]
328\f[ 0 \leq f(uv) \leq cap(uv) \quad \forall uv\in A \f]
[50]330LEMON contains several algorithms for solving maximum flow problems:
[406]331- \ref EdmondsKarp Edmonds-Karp algorithm.
332- \ref Preflow Goldberg-Tarjan's preflow push-relabel algorithm.
333- \ref DinitzSleatorTarjan Dinitz's blocking flow algorithm with dynamic trees.
334- \ref GoldbergTarjan Preflow push-relabel algorithm with dynamic trees.
[406]336In most cases the \ref Preflow "Preflow" algorithm provides the
337fastest method for computing a maximum flow. All implementations
338provides functions to also query the minimum cut, which is the dual
339problem of the maximum flow.
[314]343@defgroup min_cost_flow Minimum Cost Flow Algorithms
[40]344@ingroup algs
[50]346\brief Algorithms for finding minimum cost flows and circulations.
[609]348This group contains the algorithms for finding minimum cost flows and
351The \e minimum \e cost \e flow \e problem is to find a feasible flow of
352minimum total cost from a set of supply nodes to a set of demand nodes
[609]353in a network with capacity constraints (lower and upper bounds)
354and arc costs.
[406]355Formally, let \f$G=(V,A)\f$ be a digraph,
356\f$lower, upper: A\rightarrow\mathbf{Z}^+_0\f$ denote the lower and
[609]357upper bounds for the flow values on the arcs, for which
358\f$0 \leq lower(uv) \leq upper(uv)\f$ holds for all \f$uv\in A\f$.
[406]359\f$cost: A\rightarrow\mathbf{Z}^+_0\f$ denotes the cost per unit flow
[609]360on the arcs, and \f$sup: V\rightarrow\mathbf{Z}\f$ denotes the
361signed supply values of the nodes.
362If \f$sup(u)>0\f$, then \f$u\f$ is a supply node with \f$sup(u)\f$
363supply, if \f$sup(u)<0\f$, then \f$u\f$ is a demand node with
364\f$-sup(u)\f$ demand.
365A minimum cost flow is an \f$f: A\rightarrow\mathbf{Z}^+_0\f$ solution
366of the following optimization problem.
[609]368\f[ \min\sum_{uv\in A} f(uv) \cdot cost(uv) \f]
369\f[ \sum_{uv\in A} f(uv) - \sum_{vu\in A} f(vu) \geq
370    sup(u) \quad \forall u\in V \f]
371\f[ lower(uv) \leq f(uv) \leq upper(uv) \quad \forall uv\in A \f]
[609]373The sum of the supply values, i.e. \f$\sum_{u\in V} sup(u)\f$ must be
374zero or negative in order to have a feasible solution (since the sum
375of the expressions on the left-hand side of the inequalities is zero).
376It means that the total demand must be greater or equal to the total
377supply and all the supplies have to be carried out from the supply nodes,
378but there could be demands that are not satisfied.
379If \f$\sum_{u\in V} sup(u)\f$ is zero, then all the supply/demand
380constraints have to be satisfied with equality, i.e. all demands
381have to be satisfied and all supplies have to be used.
383If you need the opposite inequalities in the supply/demand constraints
384(i.e. the total demand is less than the total supply and all the demands
385have to be satisfied while there could be supplies that are not used),
386then you could easily transform the problem to the above form by reversing
387the direction of the arcs and taking the negative of the supply values
388(e.g. using \ref ReverseDigraph and \ref NegMap adaptors).
389However \ref NetworkSimplex algorithm also supports this form directly
390for the sake of convenience.
392A feasible solution for this problem can be found using \ref Circulation.
394Note that the above formulation is actually more general than the usual
395definition of the minimum cost flow problem, in which strict equalities
396are required in the supply/demand contraints, i.e.
398\f[ \sum_{uv\in A} f(uv) - \sum_{vu\in A} f(vu) =
399    sup(u) \quad \forall u\in V. \f]
401However if the sum of the supply values is zero, then these two problems
402are equivalent. So if you need the equality form, you have to ensure this
403additional contraint for the algorithms.
405The dual solution of the minimum cost flow problem is represented by node
406potentials \f$\pi: V\rightarrow\mathbf{Z}\f$.
407An \f$f: A\rightarrow\mathbf{Z}^+_0\f$ feasible solution of the problem
408is optimal if and only if for some \f$\pi: V\rightarrow\mathbf{Z}\f$
409node potentials the following \e complementary \e slackness optimality
410conditions hold.
412 - For all \f$uv\in A\f$ arcs:
413   - if \f$cost^\pi(uv)>0\f$, then \f$f(uv)=lower(uv)\f$;
414   - if \f$lower(uv)<f(uv)<upper(uv)\f$, then \f$cost^\pi(uv)=0\f$;
415   - if \f$cost^\pi(uv)<0\f$, then \f$f(uv)=upper(uv)\f$.
416 - For all \f$u\in V\f$:
417   - if \f$\sum_{uv\in A} f(uv) - \sum_{vu\in A} f(vu) \neq sup(u)\f$,
418     then \f$\pi(u)=0\f$.
420Here \f$cost^\pi(uv)\f$ denotes the \e reduced \e cost of the arc
421\f$uv\in A\f$ with respect to the node potentials \f$\pi\f$, i.e.
422\f[ cost^\pi(uv) = cost(uv) + \pi(u) - \pi(v).\f]
424All algorithms provide dual solution (node potentials) as well
425if an optimal flow is found.
427LEMON contains several algorithms for solving minimum cost flow problems.
428 - \ref NetworkSimplex Primal Network Simplex algorithm with various
429   pivot strategies.
430 - \ref CostScaling Push-Relabel and Augment-Relabel algorithms based on
431   cost scaling.
432 - \ref CapacityScaling Successive Shortest %Path algorithm with optional
[406]433   capacity scaling.
[609]434 - \ref CancelAndTighten The Cancel and Tighten algorithm.
435 - \ref CycleCanceling Cycle-Canceling algorithms.
437Most of these implementations support the general inequality form of the
438minimum cost flow problem, but CancelAndTighten and CycleCanceling
439only support the equality form due to the primal method they use.
441In general NetworkSimplex is the most efficient implementation,
442but in special cases other algorithms could be faster.
443For example, if the total supply and/or capacities are rather small,
444CapacityScaling is usually the fastest algorithm (without effective scaling).
[314]448@defgroup min_cut Minimum Cut Algorithms
[209]449@ingroup algs
[50]451\brief Algorithms for finding minimum cut in graphs.
453This group describes the algorithms for finding minimum cut in graphs.
[406]455The \e minimum \e cut \e problem is to find a non-empty and non-complete
456\f$X\f$ subset of the nodes with minimum overall capacity on
457outgoing arcs. Formally, there is a \f$G=(V,A)\f$ digraph, a
458\f$cap: A\rightarrow\mathbf{R}^+_0\f$ capacity function. The minimum
[50]459cut is the \f$X\f$ solution of the next optimization problem:
[210]461\f[ \min_{X \subset V, X\not\in \{\emptyset, V\}}
[406]462    \sum_{uv\in A, u\in X, v\not\in X}cap(uv) \f]
[50]464LEMON contains several algorithms related to minimum cut problems:
[406]466- \ref HaoOrlin "Hao-Orlin algorithm" for calculating minimum cut
467  in directed graphs.
468- \ref NagamochiIbaraki "Nagamochi-Ibaraki algorithm" for
469  calculating minimum cut in undirected graphs.
470- \ref GomoryHuTree "Gomory-Hu tree computation" for calculating
471  all-pairs minimum cut in undirected graphs.
473If you want to find minimum cut just between two distinict nodes,
[406]474see the \ref max_flow "maximum flow problem".
[314]478@defgroup graph_prop Connectivity and Other Graph Properties
[40]479@ingroup algs
[50]480\brief Algorithms for discovering the graph properties
[50]482This group describes the algorithms for discovering the graph properties
483like connectivity, bipartiteness, euler property, simplicity etc.
485\image html edge_biconnected_components.png
486\image latex edge_biconnected_components.eps "bi-edge-connected components" width=\textwidth
[314]490@defgroup planar Planarity Embedding and Drawing
[40]491@ingroup algs
[50]492\brief Algorithms for planarity checking, embedding and drawing
[210]494This group describes the algorithms for planarity checking,
495embedding and drawing.
497\image html planar.png
498\image latex planar.eps "Plane graph" width=\textwidth
[314]502@defgroup matching Matching Algorithms
[40]503@ingroup algs
[50]504\brief Algorithms for finding matchings in graphs and bipartite graphs.
[50]506This group contains algorithm objects and functions to calculate
[40]507matchings in graphs and bipartite graphs. The general matching problem is
[83]508finding a subset of the arcs which does not shares common endpoints.
[40]510There are several different algorithms for calculate matchings in
511graphs.  The matching problems in bipartite graphs are generally
512easier than in general graphs. The goal of the matching optimization
[406]513can be finding maximum cardinality, maximum weight or minimum cost
[40]514matching. The search can be constrained to find perfect or
515maximum cardinality matching.
[406]517The matching algorithms implemented in LEMON:
518- \ref MaxBipartiteMatching Hopcroft-Karp augmenting path algorithm
519  for calculating maximum cardinality matching in bipartite graphs.
520- \ref PrBipartiteMatching Push-relabel algorithm
521  for calculating maximum cardinality matching in bipartite graphs.
522- \ref MaxWeightedBipartiteMatching
523  Successive shortest path algorithm for calculating maximum weighted
524  matching and maximum weighted bipartite matching in bipartite graphs.
525- \ref MinCostMaxBipartiteMatching
526  Successive shortest path algorithm for calculating minimum cost maximum
527  matching in bipartite graphs.
528- \ref MaxMatching Edmond's blossom shrinking algorithm for calculating
529  maximum cardinality matching in general graphs.
530- \ref MaxWeightedMatching Edmond's blossom shrinking algorithm for calculating
531  maximum weighted matching in general graphs.
532- \ref MaxWeightedPerfectMatching
533  Edmond's blossom shrinking algorithm for calculating maximum weighted
534  perfect matching in general graphs.
536\image html bipartite_matching.png
537\image latex bipartite_matching.eps "Bipartite Matching" width=\textwidth
[314]541@defgroup spantree Minimum Spanning Tree Algorithms
[40]542@ingroup algs
[50]543\brief Algorithms for finding a minimum cost spanning tree in a graph.
[50]545This group describes the algorithms for finding a minimum cost spanning
[406]546tree in a graph.
[314]550@defgroup auxalg Auxiliary Algorithms
[40]551@ingroup algs
[50]552\brief Auxiliary algorithms implemented in LEMON.
[50]554This group describes some algorithms implemented in LEMON
555in order to make it easier to implement complex algorithms.
[314]559@defgroup approx Approximation Algorithms
560@ingroup algs
[50]561\brief Approximation algorithms.
[50]563This group describes the approximation and heuristic algorithms
564implemented in LEMON.
568@defgroup gen_opt_group General Optimization Tools
569\brief This group describes some general optimization frameworks
570implemented in LEMON.
572This group describes some general optimization frameworks
573implemented in LEMON.
[314]577@defgroup lp_group Lp and Mip Solvers
[40]578@ingroup gen_opt_group
579\brief Lp and Mip solver interfaces for LEMON.
581This group describes Lp and Mip solver interfaces for LEMON. The
582various LP solvers could be used in the same manner with this
[314]587@defgroup lp_utils Tools for Lp and Mip Solvers
[40]588@ingroup lp_group
[50]589\brief Helper tools to the Lp and Mip solvers.
591This group adds some helper tools to general optimization framework
592implemented in LEMON.
596@defgroup metah Metaheuristics
597@ingroup gen_opt_group
598\brief Metaheuristics for LEMON library.
[50]600This group describes some metaheuristic optimization tools.
[209]604@defgroup utils Tools and Utilities
[50]605\brief Tools and utilities for programming in LEMON
[50]607Tools and utilities for programming in LEMON.
611@defgroup gutils Basic Graph Utilities
612@ingroup utils
[50]613\brief Simple basic graph utilities.
615This group describes some simple basic graph utilities.
619@defgroup misc Miscellaneous Tools
620@ingroup utils
[50]621\brief Tools for development, debugging and testing.
623This group describes several useful tools for development,
[40]624debugging and testing.
[314]628@defgroup timecount Time Measuring and Counting
[40]629@ingroup misc
[50]630\brief Simple tools for measuring the performance of algorithms.
632This group describes simple tools for measuring the performance
[40]633of algorithms.
637@defgroup exceptions Exceptions
638@ingroup utils
[50]639\brief Exceptions defined in LEMON.
641This group describes the exceptions defined in LEMON.
645@defgroup io_group Input-Output
[50]646\brief Graph Input-Output methods
[209]648This group describes the tools for importing and exporting graphs
[314]649and graph related data. Now it supports the \ref lgf-format
650"LEMON Graph Format", the \c DIMACS format and the encapsulated
651postscript (EPS) format.
[351]655@defgroup lemon_io LEMON Graph Format
[40]656@ingroup io_group
[314]657\brief Reading and writing LEMON Graph Format.
[210]659This group describes methods for reading and writing
[236]660\ref lgf-format "LEMON Graph Format".
[314]664@defgroup eps_io Postscript Exporting
[40]665@ingroup io_group
666\brief General \c EPS drawer and graph exporter
[50]668This group describes general \c EPS drawing methods and special
[209]669graph exporting tools.
[388]673@defgroup dimacs_group DIMACS format
674@ingroup io_group
675\brief Read and write files in DIMACS format
677Tools to read a digraph from or write it to a file in DIMACS format data.
[351]681@defgroup nauty_group NAUTY Format
682@ingroup io_group
683\brief Read \e Nauty format
[351]685Tool to read graphs from \e Nauty format data.
[40]689@defgroup concept Concepts
690\brief Skeleton classes and concept checking classes
692This group describes the data/algorithm skeletons and concept checking
693classes implemented in LEMON.
695The purpose of the classes in this group is fourfold.
[318]697- These classes contain the documentations of the %concepts. In order
[40]698  to avoid document multiplications, an implementation of a concept
699  simply refers to the corresponding concept class.
701- These classes declare every functions, <tt>typedef</tt>s etc. an
[318]702  implementation of the %concepts should provide, however completely
[40]703  without implementations and real data structures behind the
704  interface. On the other hand they should provide nothing else. All
705  the algorithms working on a data structure meeting a certain concept
706  should compile with these classes. (Though it will not run properly,
707  of course.) In this way it is easily to check if an algorithm
708  doesn't use any extra feature of a certain implementation.
710- The concept descriptor classes also provide a <em>checker class</em>
[50]711  that makes it possible to check whether a certain implementation of a
[40]712  concept indeed provides all the required features.
714- Finally, They can serve as a skeleton of a new implementation of a concept.
718@defgroup graph_concepts Graph Structure Concepts
719@ingroup concept
720\brief Skeleton and concept checking classes for graph structures
[50]722This group describes the skeletons and concept checking classes of LEMON's
[40]723graph structures and helper classes used to implement these.
727@defgroup map_concepts Map Concepts
728@ingroup concept
729\brief Skeleton and concept checking classes for maps
731This group describes the skeletons and concept checking classes of maps.
735\anchor demoprograms
[406]737@defgroup demos Demo Programs
739Some demo programs are listed here. Their full source codes can be found in
740the \c demo subdirectory of the source tree.
[41]742It order to compile them, use <tt>--enable-demo</tt> configure option when
743build the library.
[406]747@defgroup tools Standalone Utility Applications
[209]749Some utility applications are listed here.
751The standard compilation procedure (<tt>./configure;make</tt>) will compile
[209]752them, as well.
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